Elsevier, Journal of Combinatorial Theory, Series A, 2(72), p. 340-344, 1995
DOI: 10.1016/0097-3165(95)90073-x
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A large class A of finite algorithms for fairly dividing a cake using k of fewer cuts is described. Assume an algorithm assigns piece Xi to player Pi using associated probability measure μi on measurable subsets of the cake X. If M(n, k) = max mini(μi(Xi)) and N(n, k) = max(number of i such that ) then for , for n ⩾ 3, , and for n ⩾ 4, . Also N(2n − 2, n − 1) = n.